The liquid cooling plate is critical for ensuring the safe and efficient operation of transformers, particularly in confined environments. In recent years, researchers have made significant strides in enhancing transformer cooling efficiency to address challenges posed by aging infrastructure. However, conventional serpentine-channel cooling plates suffer from significant limitations in thermal performance and flow efficiency. This study proposes a density-based topology optimization framework to overcome fixed-configuration constraints, utilizing the SIMP (Solid Isotropic Material with Penalization) method where material density serves as a continuous design variable. By penalizing intermediate densities through the power-law relation, the method drives solutions toward near-binary material distributions while maximizing heat exchange and minimizing flow resistance. The results provide a novel approach for enhancing heat dissipation in transformer cooling systems, offering potential improvements in both energy efficiency and operational safety.